SOLUTION: Please Help!!!! Which of the following is equivalent to 1/(1-cos(x))- 1/(1+cos(x))? A) 2cot(x)csc(x) B) 2tan(x)sec(x) C) 2+cot^2(x) D) 4sec(4x) E) 0 When I subtract I get

Algebra ->  Trigonometry-basics -> SOLUTION: Please Help!!!! Which of the following is equivalent to 1/(1-cos(x))- 1/(1+cos(x))? A) 2cot(x)csc(x) B) 2tan(x)sec(x) C) 2+cot^2(x) D) 4sec(4x) E) 0 When I subtract I get       Log On


   

Question 973828: Please Help!!!!
Which of the following is equivalent to 1/(1-cos(x))- 1/(1+cos(x))?
A) 2cot(x)csc(x)
B) 2tan(x)sec(x)
C) 2+cot^2(x)
D) 4sec(4x)
E) 0
When I subtract I get (1+cos(x))-(1-cos(x))/(1-cos(x))(1+cos(x)). That gives me 2cos(x)/1-cos^2(x). That's all I got. I can not figure where to go from here.
Found 2 solutions by Alan3354, Edwin McCravy:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Which of the following is equivalent to 1/(1-cos(x))- 1/(1+cos(x))?
A) 2cot(x)csc(x)
B) 2tan(x)sec(x)
C) 2+cot^2(x)
D) 4sec(4x)
E) 0
When I subtract I get
2cos(x)/1-cos^2(x)
= 2cos(x)/sin^2(x)
= 2(cos/sin)(1/sin)
= 2cot(x)*csc(x)

Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!
 
Remember the identity: sin%5E2%28theta%29%2Bcos%5E2%28theta%29=1?
Subtract cos%5E2%28theta%29 from both sides and get sin%5E2%28theta%29=1-cos%5E2%28theta%29  

The right side of that shows that the denominator of what you have so far
is sin%5E2%28x%29

2cos%28x%29%2F%281-cos%5E2%28x%29%29 becomes:

2cos%28x%29%2Fsin%5E2%28x%29

Change the choices to all sines and cosines until you find
which one is equivalent.  Begin with A)

A) 2cot(x)csc(x)

2%28cos%28x%29%2Fsin%28x%29%29%281%2Fsin%28x%29%29

2cos%28x%29%2Fsin%5E2%28x%29

So A) happens to be the correct choice.

We were lucky to get it on the first try.  If that had not
been the correct choice we would have changed the others to
sines and cosines, until we found the correct choice.

Edwin